what is the simplest radical form of 648

Since  648  =  4 x 81 x 2,

√( 648 )  =  √( 4 x 81 x 2)  =  √4 x √81 x √2  =  2 x 9 x √2  =  18√2

Prime factor 648.

$${\frac{{\mathtt{648}}}{{\mathtt{2}}}} = {\mathtt{324}}$$

$${\frac{{\mathtt{324}}}{{\mathtt{2}}}} = {\mathtt{162}}$$

$${\frac{{\mathtt{162}}}{{\mathtt{2}}}} = {\mathtt{81}}$$

$${\frac{{\mathtt{81}}}{{\mathtt{3}}}} = {\mathtt{27}}$$

$${\frac{{\mathtt{27}}}{{\mathtt{3}}}} = {\mathtt{9}}$$

$${\frac{{\mathtt{9}}}{{\mathtt{3}}}} = {\mathtt{3}}$$

$${{\mathtt{2}}}^{{\mathtt{3}}}{\mathtt{\,\times\,}}{{\mathtt{3}}}^{{\mathtt{4}}} = {\mathtt{648}}$$

2^3 can be rewritten as 2^2 * 2^1, one 2 stays in the radical. 

3^4 can be taken completely taken out of the radical as 9. 

Which becomes 2*9 √2 or 18*√2